https://file.aiquickdraw.com/mathbot/file/173032195713749dc0jcm.jpg

To graph the line represented by the equation \( y = -x - 6 \), follow these steps:

1. **Identify the Slope and Y-intercept**: 
   - The equation is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Here, \( m = -1 \) and \( b = -6 \). So, the slope is \(-1\) and the y-intercept is \(-6\).

2. **Plot the Y-intercept**: 
   - Start by plotting the point \((0, -6)\) on the graph. This is where the line crosses the y-axis.

3. **Use the Slope to Find Another Point**:
   - The slope \(-1\) means that for every 1 unit you move to the right on the x-axis, you move 1 unit down on the y-axis.
   - From the point \((0, -6)\), move 1 unit right (to \(x = 1\)) and 1 unit down (to \(y = -7\)), giving you the point \((1, -7)\).

4. **Draw the Line**:
   - Using the points \((0, -6)\) and \((1, -7)\), draw a straight line through them. This line extends across the graph in both directions.

This will create the graph for the line \( y = -x - 6 \).

Would you like further details on graphing lines, or do you have any questions?

---

### Related Questions:
1. How do you determine the slope and y-intercept from an equation?
2. What steps would change if the slope were positive?
3. How can you graph a line using the x-intercept and y-intercept?
4. What happens to the line if you change the equation to \( y = -2x - 6 \)?
5. How do you convert between different forms of linear equations?

---

**Tip:** When the slope is negative, the line falls from left to right.

Graph the line with the equation y = -x - 6.

Learn how to graph the linear equation y = -x - 6 by identifying the slope and y-intercept. Follow a step-by-step approach to plot points and draw the line, covering key concepts in linear equations and slope-intercept form. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation